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Question

If $$AB = 12$$ cm, $$BC = 16$$ cm and $$AB$$ is perpendicular to $$BC$$, then the radius of the circle passing through the points $$A$$, $$B$$ and $$C$$ is:


A
6 cm
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B
8 cm
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C
10 cm
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D
12 cm
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Solution

The correct option is C $$10\ cm$$

Given- $$A, B$$ &  $$C$$ are points such that $$AB=12cm$$ and $$BC=16cm$$  and $$BC\bot AB$$.

To find out- the radius of the circle passing through $$A, B$$ &  $$C=?$$

Solution- $$BC\bot AB$$ i.e $$\angle ABC={ 90 }^{ 0 }$$ and $$\Delta ABC$$ is a right one with $$AC$$ as hypotenuse. $$\therefore  AC=\sqrt { { AB }^{ 2 }+{ BC }^{ 2 } } =\sqrt { { 12 }^{ 2 }+{ 16 }^{ 2 } } cm=20cm$$. So the circle passing through $$A, B$$ &  $$C$$ will have its  diameter as $$AC$$.

$$\therefore$$  Its radius$$=\dfrac { 1 }{ 2 } \times 20cm=10cm.$$

Ans- Option C.


205360_77942_ans_7b5c12f1a0cd4286a6b98f8b1fff28cd.png

Mathematics

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